Analysis of Boeing 737 MAX 9 Door Plug Accident

I follow aviation accidents pretty closely. For as long as I can remember, I have been fascinated with air and space travel and the associated risks. I even took a flying lesson at Teterboro airport 15 years ago or so, but I never got a chance to get certified.

The latest Boeing 737 Max 9 accident¹ resulted in no loss of life, but the idea of a door, even a fake door, blowing out mid-flight warrants a little analysis. Some questions come to mind: How could this happen, why it happened, under what conditions (the proximal cause), and what could have happened under slightly different conditions? First, a warning: this is not an analysis of how the defect was introduced during manufacturing and assembly; I know nothing about that. This is an analysis of the conditions under which a loose door (I will call that, even though it was technically a door plug) could separate from the fuselage.

The Facts

On January 5, 2024, at 5:00 p.m. local time, Alaska Airlines Flight 1282 took off from Portland International Airport en route to Ontario, California. The sunset was at 5:25 p.m., so it was already fairly dark. When the aircraft reached approximately 16,300 feet (about 5,000 meters), the passengers heard a loud boom as the door blew out from the side of the aircraft.

Everyone on board survived, and the aircraft landed in Portland shortly after, but I am sure most passengers will have a different experience with air travel from that point forward. Many years ago, I was in a much less dangerous but scary landing that did not go as planned (no, not the runway miss with a fly-around, which I experienced twice and is not a big deal), but something more extreme. Since then, I have never been entirely comfortable during unexpected turbulence.

Conditions at 16,300 Feet and Above

The air temperature at this altitude is approximately 0 F (-17 C), and outside air pressure is about 54 kPa (kilo-Paskals) or about 8 PSI (pounds per square inch). For reference, sea-level air pressure is about 101 kPa or 15 PSI. This pressure is the column of air pushing on you as you stand on the ground, and by convention, this gives us yet another unit of pressure — 1 atm (atmosphere). Pressure is related to the number of air molecules available for each breath since the pressure is directly proportional to the density (this comes from the ideal gas law, which I will touch on later). At the cruising altitude of 33,000 feet (about 10,000 meters), the air temperature is about -50 (here, C and F units are close to each other), and air pressure is about 19.3 kPA.

At 8,000 feet and higher, there are not enough air molecules for most people to breathe, so modern aircraft are pressurized (sealed with cabin pressure controlled by the Environmental Control System).

Ideal gas law and what happens during the change in altitude

The fact the door blew out during the ascent was no accident, pardon the pun, and can be explained by the ideal gas law.

\[
pV = nRT
\]

The key quantities are Pressure $p$, Volume $V$, and Temperature $T$. The other quantities are constants, so we can write:

\[
pV \propto T
\]

From the ideal gas law, pressure is inversely proportional to volume—as pressure decreases, the volume of gas increases, and vice versa. This makes some intuitive sense, as you can imagine what happens when you reduce the volume of a sealed container; the pressure inside goes up and vice versa.

When the pressure outside the sealed container rises, say during a submerging process, the walls experience an inward pressure due to a pressure differential, and when the outside pressure falls, say during an ascent, the wall experiences an outward pressure.

This is why, during a scuba lesson, you are told to keep your mouth open on the ascent so that expanding air doesn’t damage your lungs. For the same reason, when a flight attendant hands you a bag of chips at 30,000 feet, the bag appears inflated².

This outward pressure on the fuselage caused the blowout, and we will now try to estimate how much pressure it took for the door to separate.

Computing the pressure on the fuselage

As a statistician, it always blows my mind how much we can learn from n=1 “experiments” if we are willing to bring some background knowledge, the ideal gas law in this case, to bear on the problem. Physicists would not be impressed, as to them, this is par for the course.

Anyway, back to our problem. To make the calculations, we need to make a couple of key assumptions, namely the pressure outside the aircraft as it climbs and the pressure inside the cabin. The drop in atmospheric pressure with altitude is well-known and follows an exponential decay according to the Barometric formula. This is the blue line in the following diagram.

The green and red horizontal bard indicate my error in assuming gradual cabin pressurization. The dashed line represents the altitude at the time of the accident.

The second assumption we need is the pressure inside the cabin. First, I assume that the target inside pressure is equivalent to about 6,000 feet (1,800 meters), which is at the lower end of the reported range. This type of pressurization balances the passengers’ comfort with the force that the fuselage has to withstand.

Second, I (erroneously) assumed that the pressure is gradually adjusted to reach the target at the cruising altitude of 33,000 feet, the green curve on the above diagram. I later learned that the target pressure is typically reached relatively quickly after takeoff and that the cabin pressure was most likely at its target at the time of the accident. This means that my green curve would drop much more quickly and remain flat for the rest of the flight. The green and red vertical bars at the height of the accident represent this error.

To compute the outward pressure on the fuselage (red), we take the difference between the two curves at 16,300 feet, which gives us 26 kPa, assuming the aircraft was pressurized to about 1,800 meters at the time of the accident. (If we incorrectly assume gradual pressurization, the pressure would be about 36 kPa.)

To make this more interpretable, we can compute how much force (in lb or kg-equivalent units) was applied to the door. We will assume the door is nearly rectangular with 72 x 34 inches (183 x 86 cm) dimensions, taken from a 737 manual. To compute the weight in pounds:

\[
W = P \cdot A \cdot 2.2/g
\]

P is the pressure in kPa, A is the area in square meters, and g is the gravitation constant. This turns out to be about 9,400 lb (4,300 kg), which I rounded to 9,000 lb in the diagram. At the cruising altitude of 10,000 meters, the weight on the door would be approximately 19,000 lb (~ 8,600 kg).

Conclusions

When the aircraft finally landed, the passengers were treated to the following view of the airfield.

The calculations can make us appreciate how much force every 1.6 square meters of fuselage must withstand, so constructing a well-pressurized cabin is an impressive engineering achievement, while forgetting to put a few screws into the door plug during a final assembly is a massive management oversight.

One can imagine a situation where the door was a bit more secure than it was (but still not fully installed) and that the separation would have happened at 33,000 feet instead of at 16,000. What then? I am not sure what the immediate depressurization at that altitude would do to a human body (if your mouth and nose are closed, your lungs may rupture; you may also suffer from decompression sickness; if you don’t put on the oxygen mask, you will suffocate), much less if the pilots could descend fast enough to avoid hypothermia and other pleasantries.

Up or Down

In June 2023, a submersible operated by OceanGate imploded near the remains of the Titanic. The Titanic is located at 12,500 feet (3,800 meters) under the sea, and the pressure at that depth is about 38,000 kPa, 380 times more than at the surface (~ 380 atmospheres). When the implosion was originally detected, the Coast Guard undertook a massive search and rescue operation. The rescue part was a fool’s errand — at this pressure, the passengers were instantly disintegrated.

In 2019 and 2020, the 737 Max was involved in two accidents relating to the angle of attack sensors. ↩︎
Why should the bag inflate inside the plane? That’s a good question, and this should be the clue that the cabin’s pressure is not kept at sea level but adjusted downward as the plane climbs. ↩︎

Brighter days ahead

As the dark and frustrating 2020 is winding down, I feel incredibly optimistic about 2021 and beyond. Part of it is my entrepreneurial nature that requires it and part of it is a number of recent developments that bring me hope and I love drinking hope for breakfast.

A number of recent readouts from SARS-CoV-2 trials, particularly those from Pfizer and Moderna, which use a novel mRNA platform, look efficacious and safe in the short-term. (Long-term safety can not be evaluated in rapid clinical trials but the FDA guidelines provide for long-term, post-licensure, safety monitoring.) As soon as these vaccines are made available to the general public and assuming no major safety issues are surfaced, I am getting vaccinated and resuming my pre-pandemic travel schedule.

In case you missed it, on May 30th we witnessed the first American manned space flight since 2011. I watched it in real-time that Saturday and then many more times with my son Andrei who just loves watching rockets being launched into space. Since then, watching launches on Saturdays became a Novik family tradition. Seeing Andrei’s eyes light up every time we do it, brings me an unreasonable amount of joy.

Two weeks ago I ordered my first Virtual Reality headset — Oculus Quest 2. I don’t love the Facebook login requirement but as a newcomer to the world of VR, I am completely blown away by how easily my senses are fooled and by the near-perfect rendering of 3D worlds. It is clear to me that VR is a major technological trend with ramifications far beyond gaming. I can’t wait to virtually sit in front of my family and friends all over the world and interact with them as if we are in the same room. The technology is not quite there to make the experience realistic but I have little doubt that it’s coming. (As a side note, the game Room in VR is nothing short of amazing.)

During the summer, we made a lot of progress at Generable with fitting large meta-analytic models for oncology drugs, and our abstract was accepted at SITC 2020, an immuno-oncology conference. This is a big deal for us as it represents the first publication outside of statistics journals. Most of the work was done by Jacqueline Buros and Krzysztof Sakrejda and is a culmination of our year-long research collaboration with AstraZeneca.

And if this is not enough, 2021 promises to be a much more sane US Federal Government with adults finally taking over and mitigating the Fifth Risk. No doubt countless problems remain (I don’t want to list them) but I am feeling lucky and optimistic.

Looking back at 2019

As 2019 was closing I had a feeling that I had not done that much during the year. But then I started looking over my journal entries, my photographs, the books I read (mostly listened to), the progress we made at Generable, and I realized that I did get some things done and experienced joy (and sometimes agony) along the way.

I started the year by going to see The Jungle, a play that plants you in the middle of the Calais Jungle and follows the lives of refugees struggling for survival. Jacki and I came away deeply moved by the experience.

Later in January Colleen Chien invited Dan, Jim Savage, and me to give a short talk at her class at Columbia Law School to discuss facts and fiction in AI/ML ecosystem today. I mostly focused on our work with Stan in Clinical Research and how probabilistic modeling is making it possible to construct models that are explainable, transparent, and perform very well predictively, especially if we are able to approximate the data generating process well.

In early February we celebrated Andrei’s first birthday. I never thought that I would be a father again but Andrei is bringing so much joy to my life that it almost seems worth it. OK, it is worth it. I think. I am pretty sure. I love you, Andrei!

Winter came in March to our neighborhood and we had some fun times in the snow. Andrei loves being outside and I can not wait until he is old enough to go skiing with us.

In early March, Generable had our first off-site in Pocono Pines. This is when started seriously thinking about what product we wanted to build. At the time we thought we are going to make a tool for Stats and Data Science types to build models from different components. That turned out to be wrong. More on that later.

In the middle of March, my oldest son Ben and I built a computer from individual parts. He was surprisingly enthusiastic about this enterprise and I enjoyed working with him on this. When we turned it on and loaded the OS (Ubuntu) it became obvious that the project succeeded. Ben had not used this computer since and I turn it on only occasionally but the whole experience was totally worth it. Thanks, Ben for putting up with my relentless pursuit to turn you into a nerd.

Later in March, we saw another play at St Ann’s Warehouse called The B-Side. This play is a musical in an off-broadway sense of the word. The main character sings along a vinyl album containing songs by African American convicts in a Texas prison. I love seeing this kind of production making it to the serious stage and selling out a large theater in Brooklyn.

At the end of March, we went to see Marys Seacole (based on the life of Mary Seacole) at the Lincoln Center. The story follows Mary throughout her life and to the battlefield of the Crimean War. I don’t remember a lot of details from that play; perhaps it did not leave an impression on me or I just drank too much bourbon shortly thereafter.

In April, I was invited to be on a panel with other alumni of the Columbia Univesity’s MA in Statistics program. I love coming back to the stats department and talking to current students and recent graduates. I usually tell them to learn some Bayesian stats — most of them will graduate without encountering a posterior distribution. A tragic state of affairs, but that’s how it is for now.

Later that month, we started re-designing the Generable platform and focusing on what we call the Clinical Lead — the person who oversees early clinical trials and gives an opinion of whether a treatment should advance to a late-stage clinical trial. Inside a Pharma company, this is not just a clinical decision, there are economic factors at work, but the clinician makes an assessment of the drug is working. We abandoned the model-building idea and instead embraced communicating model results and supporting decision-makers.

At the end of April, we went to see Oklahoma on Broadway. I know people love this musical, but something about it did not click for me. I love that it is made and I think I understand the scope, but I could not quite grow to love it.

In early May I was visiting a colleague in Northampton where we have a small office. I was staying in an Airbnb house inhabited by an artsy old lady.

“What do you do?” she asked me one evening when I came home late, slightly drunk.

“I am a Statistician working in clinical research, early clinical trials in Oncology.”

“Did you say Oncology?”, she asked.

“Yes”, I answered.

“Thank you for everything you do! I am a cancer survivor.”

I was completely taken aback as this never happened to me before.

“I am not a doctor, I do not treat patients, and if we make any contributions, it would be many years from now”, I told her.

This was not false modesty. I really did not feel that I deserved her thanks, not yet anyway. But she wouldn’t have it. I finally told her she is very welcome and now completely sober and slightly teary-eyed stumbled upstairs and went to bed.

Later in May, I attended and co-presented at the Bayes-Pharma conference in Lyon, France. Marmaduke Woodman from the University of Aix-Marseille and I talked about the work we did fitting Stan models to epileptic seizures data collected from electrodes implanted in patients’ brains. The hope is that these models could be used to improve the precision of surgical interventions. I think they are planning a clinical trial for later this year.

In June, I attended the PAGE (European Pharmcometrics) conference in Stockholm, and right after the conference, I caught a short flight across the Baltic Sea to visit my mother in Riga, the city of my birth. Riga is a beautiful, modern European city with manicured parks, well-maintained Art Nouveau architecture, mild weather, and tragic history.

Every year, I promise myself that I would spend some time with my parents and this year I kept my promise. We have a lot in common my mother and me, kindred spirits so to speak. For one, she is just as vulgar as me and she appreciates my not-so-kosher jokes.

On the way home, I had a stopover in Amsterdam, where I spent a few hours at the Rembrandt House Museum before taking a long flight back to New York.

In June, my daughter Miriam graduated from middle school. She worked really hard and improved her grades considerably. I was (and still am) so proud of her.

At the end of June, the Generable crew had the second off-site meeting in Denver. I like spending one week with our remote team every three months or so. It helps to get on the same page, agree on key priorities, collaborate on technical tasks, and just spend some time hanging out together.

At the beginning of August, we spent a customary week on Lake Sunapee in New Hampshire. Ben took some sailing lessons, we played some tennis, biked, played Monkey Bridge (a Buros family tradition), and generally had a nice relaxing time. I worked most of the time but it did feel like a vacation.

On the way back from Sunapee we stoped in Belchertown to break up a long drive back. In the morning, Ben and I took a 10-mile bike ride to visit the University of Massachusets at Amherst. It is a lovely suburban campus with lots of green lawns. Can you picture yourself going here, I asked Ben. I dunno, replied Ben which is his standard reply. At least he is not over-confident!

In the middle of August, the Generable crew attended StanCon in Cambridge UK, an annual conference dedicated to all things Stan. Generable was one of the sponsors and Dan and Krzysztof presented.

In September, we took Andrei to the New York Aquarium on Coney Island. They have recently renovated the place and some of the construction is still in progress.

At the end of September, Jacki, Miriam, and I went to Disney World. Miriam wanted to go for a long time and I am happy we were able to do it. The Magic Kingdom is aging and not very gracefully, but the Flight of Passage ride in the Animal Kingdom left such an impression on me that I am seriously considering getting a VR set even though the ride itself is not in VR. It’s pretty damn close to R. While in Orlando, my dad came and stayed with us for a few days, which was nice as I do not get to see him that much anymore.

In October, we showed an alpha version of the Generable platform at the ACOP conference in Orlando. This is the first time we were able to afford a booth, which is some kind of milestone. A lot of people don’t like “working the booth” but I do, particularly when the traffic is heavy which was not always the case at ACOP. Next year we should be doing more clinically oriented conferences but we will likely be back at ACOP and PAGE.

In September we went to see Slave Play, a Broadway production that is too weird to describe so I am not going to try. If you go see, and perhaps you should, it will make you very uncomfortable, which I am sure is by design.

We ended the year with the play The Sound Inside with Mary-Louise Parker (Weeds and other good stuff) in the lead role. This was my favorite play of the year and one that I will remember for a long time. Poignant references to DFW, parallels and direct references to Raskolnikov from Crime and Punishment, a masterful soliloquy by Mary-Louse, are just some of the features that made this play special for me.

This was in many ways a theatrical year.

Here is to you 2019!

My Trip to Astana, Kazakhstan

Getting There

After a 20 minute ride to the Jamaica Queens from Penn Station on the LIRR I am at the JFK. LIRR is really the best way to travel to JFK from the city. My flight leaves at 10:20 pm and the check-in procedure is quick an painless. I noticed that Lufthansa clerk did not check if I had a Kazakhstan visa.

It is approximately 7 hours to Frankfurt, one hour layover and another 5.5 hours to Astana. The flight was smooth and the airline food was surprisingly bearable. On the flight to Astana three Russian woman were sitting next to me talking about a Government congress that they were either organizing or actively participating in; their enthusiasm for navigating the local bureaucracy was noticeable but alas not infectious. Their command of the English language was impressive.

We landed in Astana at 12:30 AM local time, right on schedule. Anton, a grandson of repressed Polish people living in Russia during the Stalin era, met me at the gate. 20 minutes later we were in downtown Astana.

First day in Astana

A few hours of sleep and I was up and ready to soak in the local culture. After acquiring a local sim card and telephone for $26 (4,000 ten) we visited the Pyramid and Court of Independence. Astana has an architectural plan, displayed on the third floor of the Castle of Independence spanning 18 years through 2030. The plan is to build a capital of Asia that would rival it seems the Arab Emirates.

The Pyramid is a magnificent structure taking the shape according to its name. Several floors displaying (artwork?) culminate with a garden, leading to a small auditorium at the apex. There, the world religious congress is being held every three years and representatives from world religions meet in a friendly atmosphere. This was the first sign of religious tolerance and celebration of cultural diversity that I have encountered in Astana. It was one of many.

After visiting the Pyramid Anton and I have taken a short walk across the street to visit the Court of Independence. It is another enormous structure of marble inside and out. The interior looks so polished that the floor ornaments reflect light making me feel like I am walking on an opaque mirror. An excursion organized by the staff takes us along the atrium to a set of stairs leading to the second floor. There, a small art gallery displays the works of local, American, and French painters, none familiar to me. I am particularly fond of the local painters depicting the nomadic lifestyle of the region.

Bayterek

Bayterek was the first building that marked the beginning of the massive construction project undertaken by the president of Kazakhstan. Incidentally, his pictures and portraits are splattered all over Astana in museums, road signs, and government buildings. Normally this type of propaganda is a sign of deep political corruption, which may indeed be the case, but in Kazakhstan common people seem to have a lot of respect for the president.

When I asked a tour guide at the top of Bayterek what she thought about the planned expansion of the city, she said that it would continue due to the will and ideas of the president, “may god bless his soul”. Her opinion was seconded by Anton, albeit not as enthusiastically. He thinks that even though Nazarbaev is the king of Kazakhstan, his policies of pluralism and his support of national diversity enables the peoples from 150 or so religions and nationalities to coexist in peace and mutual respect. This is not a small feat and the president should be applauded for this, irrespective of his motives.

Visit to the Chabad House

The tour guide at Bayterek mentioned that among other religious institutions, Astana has a large synagogue. I was surprised to hear that, since I knew that very few Jews live in Kazakhstan. Naturally, I was excited to see it with my own eyes. The Astana Synagogue is in fact an impressive building of white and blue on the (Left) side of the city (Astana is divided in two informal parts by the river Ishum. The new construction is on the right bank of the river if you are facing (North?))

This Synagogue is fact part of Habad, a Hasidic organization whose mission is to attract more Jews into the religious practice. It is the only branch of orthodox Jewry that is welcoming of secular Jews. The building is guarded by a perimeter fence and a security guard at the front gate. After informing the guard that I would like to visit the Synagogue, he politely motions me inside and leads me up the stairs into the entrance. Anton follows me in.

The Synagogue is empty at 2 PM in the afternoon. The guard informs the Rabbi of our arrival and in less than 30 seconds he appears smiling, sporting an obligatory long beard, white shirt, and a Hasidic hat. He is clearly happy to see us, and after inquiring if I were Jewish (he did not ask Anton, who looks very Slavic) hands both of us a yarmulke and invites us into the prayer hall.

My guess is that the room sits approximately 50-100 people at the main level and another 20 or so on each balcony dividing the space into separate sections for men and women. Men can not focus on higher thoughts and prayers when women are too close, he explains. I think he is right about that.

After he finished explaining the building attributes, I see that his excitement is starting to grow as he informs me that a big mitzvah is about to be performed. He runs to the back and promptly returns holding a black box containing a tefillin. I am a little bit squeamish, but he is so persistent that I submit and let him wrap my left hand with a flat leather rope, while placing a wooden box on my head. I repeat his words of prayer as he performs the procedure.

When he is done, he informs me that he knows of 200-300 Jews that live in the city. For a city of 700,000 this is indeed a minority. Regular services usually gather 3-6 people and they only achieve minyan on Saturdays. Despite of a small congregation they publish a woman’s magazine and Jewish calendar. After giving Anton and I a copy of each, and asking us if we want something to eat or drink he politely escorted us back to the entrance. Please, come back whenever you are in town, he said to me. You as well, he said to Anton.

Trip to ALZHIR

Before coming to Kazakhstan I knew that if I only could visit one site in Astana it would be ALZHIR. The camp lies 20 km East of the city in a village that was called Molinovka (meaning made from raspberries). It was part of Soviet Gulag system from 1937 until shorty after Stalin’s death in 1955. The system is commonly referred to as Gulag Archipelago due to Aleksandr Solzhenitsyn. ALZHIR’s significance is not that it housed political prisoners convicted under Article 58 of the NKVD code, but that it housed their wives and children under the age of 3 (children that were 3 years old or older were separated from their mothers and their siblings and sent to a ‘det dom’: a children’s house that is roughly equivalent to a penitentiary for juvenile delinquents).

The road to ALZHIR (Akmolinki Lager’ Zhen Izmennikov Rodini: Akmolinsky Camp for the Wives of Traitors to the Motherland) is a deteriorating Soviet era asphalt road with enough bumps and cracks to ruin the suspension system of a modern tank. After about 30 minutes of bumping and grinding we arrive at the camp. As we approach the main building, the first item is in the front right – a Soviet rail car used in transporting women from all over the Soviet Union to ALZHIR.

These wagons were manufactured in Odessa, Ukraine from 1928 to 1929 and women spent more than two months inside while being transported to ALZHIR. The wagon is approximately 7×3 meters (23×10 feet) and housed over 70 prisoners. Many had to stand and sleep on top of each other.

To the left, a monument commemorating the victims.

The barracks have been destroyed and the only surviving structure is the guard tower with the museum building in the back.

Over 17,000 women were held in the camp, many have died from malnutrition and 18 hour work days. Their bodies were dumped into a mass grave behind the camp. Among the prisoners were noted Russian intellectuals and artists including Rachel Messerer, the mother of a famous Russian jewish ballerina Maya Mikhailovna Plisetskaya.

Inside the museum the story of the prisoners unfolds. While still in Moscow, the women were told by the authorities that a rendezvous with their husbands was being arranged and asked to come to the prison building for the meeting. Many were so happy that they wore red dresses and makeup in anticipation. When they arrived, they were escorted to the ‘waiting area’. Many never saw freedom again. They were read their charges, asked to admit that their husbands were traitors, separated from their children, and packed into wagons for transport to ALZHIR.

While at the camp they built their own barracks from straw and clay that could be found on the outskirts of the camp. The women also made their own clothes and later made uniforms for soldiers during the Second World War.

One day, while collecting straw, a group of local Kazakh men and women came by. They watched them work and then started throwing what appeared to be small bricks and stones at the prisoners. The guards were laughing. Even the locals know that you are traitors, they said. One of the women picked up a small brick. It was made out of bread.

When we left the camp, I asked Anton to stop in the middle of the steppe.

In March the steppe is still covered with ice as temperatures can fluctuate between -30 (c) and -10 (c). I walked on the other side of the road and stepped onto the brittle snow. Even though it looked solid, my legs went in knee deep. For a while I just stood there breathing cold air and getting lost in the serenity of infinite spaces stretching for hundreds of miles in all directions. The Kazakh flatland is calming and magnetic. How was it, asked Anton when I got back in the car. It was magical, I said. Finally, I felt like I was in Kazakhstan.